
where \(\widehat{\alpha }_{0:n}\)  denotes an estimator of the AR parameter based on the full data set.
Some authors suggest to use partial sums of estimated residuals;
however, the thus-constructed test has power only against some alternatives,
namely those leading to changes in the mean of estimated residuals (see e.g. [1]}).
The statistic in (REF ) bears clear resemblance to the CUSUM statistic
for mean change detection
(written below with slightly different location-dependent weights from Section REF 
for better comparison):
\(\frac{1}{\sqrt{n}} \max _{1 \le k < n} \left| \sum _{t = 1}^k (X_t - \bar{X}_{0:n})\right|.\) 
